Transworld Research Network 37/661 (2), Fort P.O. Trivandrum-695 023 Kerala, India
Advances in Non-Crystalline Solids: Metallic Glass Formation, Magnetic Properties and Amorphous Carbon Films, 2010: 181-202 ISBN: 978-81-7895-440-0 Editors: Herlinda Montiel and Guillermo Alvarez
7. Electron paramagnetic resonance of transition metal ions in glasses: Recent progresses Guillermo Alvarez Departamento de Materiales Metálicos y Cerámicos, Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, Coyoacan, DF, 04510, México
1. Introduction In recent years, the glasses that contain transition metal ions [1-6] are of continuous interest because of their potential applications, in the development of new tunable solid-state lasers, solar-energy converters, electrical threshold and memory switching as well as optical switching devices [7-9]. Also, the glasses that contain a magnetic phase with a biocompatible glassy matrix could be used as thermoseeds for hyperthermia treatment of cancer [10-12]; in the fact that when a magnetic glass piece is implanted close to cancerous tissue and it is exposed to an alternating magnetic field, the heat generated by magnetic hysteresis loss kills the infected tissue. On the other hand, the mixed alkali effect is one of the classic ‘anomalies’ of glass science [13-15] and has been the subject of study over the years. Many physical properties of glasses have shown a non-linear behaviour exhibiting a minimum or maximum, as a function of alkali content; Correspondence/Reprint request: Dr. Guillermo Alvarez, Departamento de Materiales Metálicos y Cerámicos Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, Coyoacan, DF, 04510, México. E-mail:
[email protected]
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if one alkali ion is gradually replaced by another alkali ion, keeping the total alkali content constant. This behaviour is called the ‘mixed alkali effect’ (MAE), and is observed for properties associated with alkali ion movement such as electrical conductivity, ionic diffusion, dielectric relaxation and internal friction [13]. In particular, the study of transition metal ions in an amorphous matrix is one of the interesting research subjects both from the theoretical and experimental points of view. The glasses containing transition metal ions possess interesting and unusual properties arising from the fact that this ion can exist in more than one valence state in glasses [16-21]. The transition metal ions can be used to probe the glass structure, because their outer d-electron orbital functions have rather broad radial distributions and their response to surrounding cations is very sensitive [22]. Additionally, by more of sixty years, since its discovery in 1944 by E. K. Zavoisky, the electron paramagnetic resonance (EPR) spectroscopy has been exploited as a very sensitive and informative technique for the investigation of different kinds of paramagnetic species in solid, as is the particular case of transition metal ions. EPR is the most powerful spectroscopic method available for obtaining detailed information on some of the structural and dynamic phenomena regarding the glass network and to identify the site symmetry around transition metal ions [23-38]. Also, changes in the composition of the glass may change the local environment of the transition metal ions incorporated into the glass, leading to ligand field changes which may be reflected in the EPR technique.
2. Fundamentals of EPR theory in glasses Let us consider the case more general, the EPR spectra in glasses, that contain transition metal ions, could be analyzed using the spin Hamiltonian [39-42] of the form: H=β g·H·S + A·S·I + D {Sz2 –[S (S+1)/3]} + E (Sx2 –Sy2)
(1)
where β is the Bohr magneton, g is the tensor of the spectroscopic-factor, H is the applied magnetic field, S is the spin operator of the electron and Sx, Sy and Sz, are components of spin along three mutually perpendicular crystalline axes x, y, and z; A is the hyperfine coupling tensor and I is the spin operator of the nucleus; and, D and E are the crystal-field parameters representing respectively axial and rhombic distortions from the cubic symmetry. The two crystal-field parameters D and E can be combined into a single parameter,
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λ = E/D; it has been shown that λ varying from 0 to l/3 covers all significant crystal field situations from fully axial (λ = 0) to fully rhombic (λ = l/3) symmetry. If D or E is large as compared with gβH, in the two limiting cases of D ≠ 0, E = 0, and D = 0, E ≠ 0, the energy levels in zero magnetic field are easily found to be three Kramers doublets. In particular, if D and E are zero and considering an axial symmetry, the spin Hamiltonian can be expressed as [40] H=βg//HzSz+ βg┴(HxSx+HySy)+A//SzIz+A┴ (SxIx + SyIy)
(2)
where g// and g┴ are the parallel and perpendicular principal components of the g tensor; A// and A┴ are the parallel and perpendicular principal components of the hyperfine coupling tensor; Hx, Hy and Hz are the components of the magnetic field; and Ix, Iy, and Iz are the components of the spin operator of the nucleus. The solutions of the spin Hamiltonian for the parallel and perpendicular hyperfine lines are [43]: H//(mI) = H//(0) – A//mI - {(63/4) - mI2} {A┴2/2 H//(0))
(3)
H┴(mI) = H┴(0)– A┴mI - {(63/4)-mI2}{A┴2 + A//2)/4 H┴(0))
(4)
where mI is the magnetic quantum number of the nucleus; H//= hν/g//β and H┴= hν/g┴β, where h is the Planck constant and ν is the frequency of the spectrometer, typically of 9.4 GHz (X-band). The H// position has to be taken in the maximum of the first derivative curve of the parallel hyperfine structure component for a give m value, while the H┴ position is enclosed between the first derivative perpendicular peak and its “zero” [16]. The spin Hamiltonian parameters are usually determined by using Eqs. (3) and (4). An iterative method for the numerical analysis of the EPR spectrum as suggested by Muncaster et al. [44] could be used to avoid the errors caused by certain amount of overlapping between hyperfine lines. From the values of these parameters, the dipolar hyperfine coupling parameter, P=2γββN and the Fermi contact interaction term, K, can be evaluated by using the relations [45]: A//= -P [K + (4/7) – ∆g// - (3/7) ∆g┴]
(5)
A┴= -P [K - (2/7) – (11/4) ∆g┴]
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where ∆g//= g//-ge, ∆g┴ = g┴-ge and ge (=2.0023) is the g-factor of free electrons [46]. The term -PK in Eqs. (5) and (6) is due to an s-character of the magnetic spin. Basically, this s-character results from the partial unpairing or polarisation of the inner s-electrons as a result of an interaction with the unpaired d-electrons [47]. From the molecular orbital theory, it can also be shown [46] that the components A// and A┴ consist of the contributions A’// and A’┴ of the 3dxy-electron to the hyperfine structure and the PK term arising due to the anomalous contribution of the s-electrons. Eqs. (5) and (6) can be rewritten in the following way: A// = -PK - P[(4/7) - ∆g// - (3/7) ∆g┴] = -PK + A’//
(7)
A┴ = -PK - P[(2/7) + (11/4) ∆g┴] = -PK + A’┴
(8)
The number of spins participating in resonance can be calculated by comparing the area under the absorption curve with regard to a standard (e.g. CuSO4·5H2O) of known concentration. Weil et al. [41] gave the following expression which includes the experimental parameters of both sample and standard. N={Ax(Scanx)2Gstd(Hmod)std(gstd2)[S(S+1)]std(Pstd)1/2}/{Astd(Scanstd)2Gx(Hmod)x (gx2)[S(S+1)]x(Px)1/2}[Std] (9) where A is the area under the absorption curve which can be obtained by double integrating the first derivative EPR absorption curve, Scan is the magnetic field corresponding to unit length of the chart, G is the gain, Hmod is the modulation field width, g is the g-factor, S is the spin of the system in its ground state and P is the power of the microwave source. The subscripts “x” and “std” represent the corresponding quantities of transition metal ions in the glass sample and the reference sample (CuSO4·5H2O), respectively; [Std] represents the number of spins in the reference sample. By using Eq. (9), the number of spins participating in resonance can be evaluated. The paramagnetic susceptibility (χ) can be calculated to a temperature, for glasses doped with transition metal ions, using the formula [48]: χ= [N g2 β2 J(J+1)]/ 3kBT
(10)
where N is the number of spins per m3, J the total angular momentum, kB the Boltzmann constant and T the absolute temperature. N can be calculated from Eq. (10) and g[=(g///3+2g┴/3)] is taken from EPR spectra.
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3. Experimental studies of glasses using EPR technique In this section, the results of studies on glasses using EPR technique are described. These examples include glasses that contain transition metal ions and alkali ions, highlighting main characteristics and illustrating as the measurements EPR is manifested in this kind of glass. 3.1. Glasses that contain Fe ions Iron ions exist in different valence states with different local symmetry in the glass matrices, for example, as Fe+3 with both tetrahedral and octahedral coordination, and/or as Fe+2 with octahedral coordination. Though Fe+3 and Fe+2 ions are both paramagnetic, only Fe+3 (3d5,6S5/2) shows EPR absorptions at room temperature [49,50]. EPR spectra of Fe+3 ions in glasses are generally characterized by the appearance of resonance absorptions at g ≈ 4.3 and 2.1, with their relative intensity being strongly dependent on composition [25,26,51-53]. The resonance line at g ≈ 4.3 is characteristic of isolated Fe+3 ions predominantly situated in rhombically distorted octahedral or tetrahedral oxygen environments. The resonances at g ≈ 2.1 are assigned to those ions which interact by a superexchange coupling, and can be considered as distributed in clusters [25,26,51-53]. In some cases, a resonance line near g ≈ 6.0 has also been observed [54-57] as a shoulder of the resonance near g ≈ 4.3. Figure 1(a) shows the EPR spectra of CaO–SiO2–P2O5–Na2O–Fe2O3 glass–ceramic with different Fe2O3 concentrations. When applying the spin Hamiltonian of Eq. (1), and considering that there is not hyperfine interaction, can be assigned the feature at g ≈ 2.0 with weak crystal field terms and the feature at g ≈ 4.3 with the rhombic distortions of the crystal field about a site of tetrahedral or octahedral symmetry. The variations in the EPR parameters, the linewidth (∆H(g= 2.0)) and the intensity (I(g= 2.0)= J ∆H2(g= 2.0)), where J is the relative peak-to-peak height), of the absorption line at g≈ 2.0 are plotted in figure 1(b), and these parameters shows an increase as function of Fe2O3 concentration. The resonance at g ≈ 2.0 is due to the formation of iron clusters which give rise to superexchange type interaction between iron ions. The increase in I(g= 2.0) as a function of iron oxide content, indicates an increase in the superexchange interactions in the glass-ceramic samples. However, the nonlinear increase of I(g= 2.0) and ∆H(g= 2.0) with Fe2O3 concentration, as is shown in figure 1(b), indicate that the iron irons are present as Fe+3 as well as Fe+2 in the sample. Fe+2 ions are not involved in the EPR absorption but their interactions with Fe+3 influence the characteristics
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Figure 1. (a) EPR spectra of 41CaO·(52-x)SiO2·4P2O5·xFe2O3·3Na2O glass–ceramic samples at room temperature; and (b) composition dependence of intensity and linewidth for absorption line to g ≈ 2.0 of glass–ceramic samples [23].
of the absorption lines. Superexchange mechanisms tend to narrow the absorption line. On the other hand, interactions between Fe+3 and Fe+2 ions tend to broaden the linewidth. Figure 2 shows the EPR spectra of 0.5 mol% of Fe+3 ions in xNa2O-(30- x) K2O-70B2O3 (5 ≤ x ≤ 25) glasses at room temperature. The EPR spectrum exhibits an intense sharp resonance signal at g ≈ 4.02, a moderately intense signal at g ≈ 2.02 and a shoulder in the region of g ≈ 7.20 for all the glass samples. The existence of the resonant signals at g ≈ 4.02 and g ≈ 7.20 are attributed to Fe+3 ions in rhombic and axial symmetry sites, respectively, in agreement with the spin Hamiltonian; while the resonance at g ≈ 2.02 is due to Fe+3 ions coupled by exchange interactions. The number of spins (N) that are participating in the resonance can be calculated by means of Eq. (9). The composition dependence of the number of spins participating in resonance for Fe+3 ions in the glasses at room temperature for the signals at g ≈ 4.02 and g ≈ 2.02 are shown in figure 2(b). It is observed that, initially it decreases with x up to x = 10 and then increases up to x = 15 exhibiting a minimum at x = 10 and a maximum at x = 15 and thereafter it gradually decreases. This type of nonlinear variation of N with x, exhibiting a minimum and maximum may be attributed to the mixed alkali effect and may be due to the conversion of Fe+3 to Fe+2 with x. The Fe+2 ions are not involved in the EPR absorption but their interaction with Fe+3 may influence the characteristics of the EPR absorption lines. The Pyrex glasses, after window glasses the most common form of commercial glasses, are a quaternary mixture of SiO2, B2O3, Al2O3 and Na2O,
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Figure 2. (a) EPR spectra of 0.5 mol% Fe+3 ions doped in different mixed alkali borate glasses-xNa2O-(30-x)K2O-70B2O3 (5 ≤ x ≤ 25)- at room temperature; (b) the variation of number of spins for resonances at g ≈ 4.02 (Ng=4.02) and g ≈ 2.02 (Ng=2.02) with concentration (x) in different mixed alkali borate glasses [34].
and these kinds of glasses typically have paramagnetic centers (defects). In figure 3 are shown EPR spectra of Pyrex glasses (sodium aluminum borosilicate glasses) at 300 K and 77 K, respectively. EPR spectra show the characteristic Fe+3 signals, g ≈ 4.3, 2.1 and 6.0; these Fe+3 ions can exist in glasses either in the substitutional sites or in the interstitial positions. The signals at g ≈ 4.3 and 6.0 are due to the tetrahedral Fe+3 ions in the substitutional silicon site under a rhombic and axial distortion, respectively, due to the presence of compensating cations (alkali ion) in its neighborhood. Figure 3 shows that the resonance line to g ≈ 2.1 is broadened compared to g ≈ 4.3. In fact, this absorption line (g ≈ 2.1) is known that appear when the iron content is sufficiently large so that the iron-iron distance to be enough small, for that the exchange interaction to be effective; these pairs of exchange coupled Fe+3 ions can arise from interstitial Fe+3 ions. From the temperature variation spectra, it is observed that the intensity of the EPR lines at g ≈ 4.3 and 6.0 increases with decreasing temperature and the linewidths for resonance lines are found to be independent of temperature; but also it is observed a broaden considerable of the resonance line at g ≈ 2.1, due to a increase of the exchange interactions at low temperature. The above-mentioned suggests that both signals are independent among them, confirming of this way the different nature of the defect.
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Figure 3. EPR spectra of Pyrex glass at (a) 300 K and (b) 77 K.
3.2. Glasses that contain Mn ions It is known that the manganese in the glass matrices exists in the form of Mn and Mn+2 [22]. The Mn+3 ions are not usually detectable by EPR technique at 9.5 GHz (X-band). EPR spectra of Mn+2 ions (3d5,6S5/2) in glasses have been known for a long time [24,58-60], and usually contain three sets of lines with values for g-factor of approximately g ≈ 4, 3, and 2. In figure 4 are shown EPR spectra of xMnO·(100-x)[B2O3·Bi2O3] glasses, due to Mn+2 ions, at different concentrations. The structure of the spectra strongly depends on the MnO content of the samples. EPR spectra consist mainly of resonance lines centered at g ≈ 4.3 and g ≈ 2.0, their relative intensity is dependent of the manganese content in the samples. For 0.3 ≤ x ≤ 3 mol%, the absorption line at g ≈ 4.3 is prevalent in the spectrum and it shows the hyperfine structure characteristic of the 55Mn (I = 5/2) isotope; and then will be necessary to apply the spin Hamiltonian of Eq. (1). Superimposed on this absorption line, the narrow line corresponding to accidental impurities of Fe+3 ions is also detected, see figure 4(a). For 5 ≤ x ≤ 20 mol% the resonance line centered at g ≈ 4.3, had not hyperfine structure (figure 4). This resonance line is due to magnetically isolated Mn+2 ions, in distorted sites of octahedral symmetry. The absorption line at g ≈ 2.0 is generally attributed to isolated Mn+2 ions in octahedral symmetric sites slightly tetragonally distorted, to the Mn+2 ions participating at the dipolar interactions or/and to superexchange coupled pairs of these ions. The absorption line at g ≈ 2.0 is prevalent in the spectrum for x ≥ 10 mol% and for this line no hyperfine structure is detected. This EPR line also depends on the MnO content of the samples. Their evolution suggests that the Mn+2 ions are involved in dipolar interaction responsible of +3
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the EPR line broadening. At higher MnO content, the dipolar broadening is balanced, by narrowing mechanisms due to superexchange type interactions between the manganese ions. But, for x > 10 mol% the narrowing of the EPR signal centered at g ≈ 2.0, can be balanced by the broadening effects due the interaction between manganese ions with mixed valance states or the progressive disordering of the glass network. So that, at high MnO content, besides the Mn+2 ions species, the only ones giving rise to EPR absorption, superior valence state of manganese ions (Mn+3) may occur in the samples. Figure 5(a) shows the EPR spectra of 0.5 mol% of Mn+2 ions in xLi2O(30-x)Na2O-69.5B2O3 (5 ≤ x ≤ 25) glasses at room temperature. These signals are due to the Mn+2 ions entering the glass network as paramagnetic species. All the glass samples show a broad resonance at g ≈ 2.0 with six line hyperfine pattern, which is a characteristic of Mn+2 ions with a nuclear spin I = 5/2. The EPR signal from g ≈ 2.0 is given by two covered signals: one signal with resolved hyperfine structure (given by the isolated Mn+2 ions) and another one signal come from the Mn+2 ions involved in dipole–dipole type interactions. The resonance line at g ≈ 2.0 is also due to an environment close to octahedral symmetry. In addition to this, a shoulder around g ≈ 3.3 and a sharp signal at g ≈ 4.3 are also observed, see figure 5(a). The resonance signal centered at g ≈ 3.3 is broad, unresolved giving a shoulder like signal. The absorption centered at g ≈ 4.3 is less intense. The resonances at g ≈ 3.3 and g ≈ 4.3 can be attributed to the rhombic surroundings of the Mn+2 ions. The number of Mn+2 ions participating in resonance at room temperature in xLi2O-(30-x)Na2O-69.5B2O3 (5 ≤ x ≤ 25) mixed alkali glasses have been calculated as a function of x by means of Eq.(9), and it is shown in figure 5(b). One can observe that N increases with x and reaches a maximum
Figure 4. EPR spectra of Mn+2 in xMnO·(100-x)[B2O3·Bi2O3] glasses for (a) 0.3 ≤ x ≤ 5 mol% and (b) 10 ≤ x ≤ 50 mol% [61].
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Figure 5. (a) EPR spectra of 0.5 mol% MnO2 doped xLi2O-(30-x)Na2O-69.5B2O3 (5 ≤ x ≤ 25) glasses, and (b) the variation of number of spins (N) as a function of alkali content in glass samples (adapted from [37]); at room temperature.
around x = 20 and thereafter it decreases showing the mixed alkali effect in LiNaB mixed alkali glasses. The variation of N can be due to the structural changes with composition and also the modification of boron network with alkali content. Additionally, the EPR spectral of 20Li2O–10Na2O–69.5B2O3 + 0.5 MnO2 glass sample are recorded at 300-123 K (see figure 6(a)) in order to study the temperature dependence of number of spins participating in resonances. Figure 6(b) shows a plot of Log(N) versus reciprocal of absolute temperature (1/T) and it is observed that it obeys Boltzmann law; i.e. it confirm the paramagnetic nature of the resonance [40-42]. 3.3. Glasses that contain Cu ions In glasses, the copper ions exist in two stable ionic states, monovalent Cu ions and divalent Cu+2 ions, and can also exist as metallic copper. The electronic structure of the copper atom is [Ar] 3d10 4s1; the cuprous ion, having its five d orbitals occupied, does not produce EPR lines, while Cu+2 ion create color centers with EPR signal [30,33,62,63]. The Cu+2 ion, with S = 1/2, has a nuclear spin I = 3/2 for both 63Cu (natural abundance 69%) and 65 Cu (natural abundance 31%) and therefore (2I+1) projections, i.e. four parallel and four perpendicular hyperfine components would be expected. +
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Figure 6. (a) EPR spectra of 20Li2O-10Na2O-69.5B2O3 + 0.5MnO2 glass sample as a function of temperature. (b) A plot of Log(N) against 1/T for the same glass sample (The solid line is a least square fit with a correlation coefficient of 0.987) [37].
It is well known that Cu+2 ions in glasses and aqueous complexes can not exist in a regular octahedral coordination. The cubic symmetry of Cu+2 ions is disturbed due to the presence of the electronic hole in the degenerate dx2-y2 orbital, exhibiting tetragonal distortion. Hence, Cu+2 ions in glasses will be predominantly in axially elongated octahedral sites. The EPR spectra of Cu+2 ions can be appropriately analyzed by using the axial spin-Hamiltonian given for Eq. (2). The EPR spectra of calcium alumino borate (CaAB) glasses doped with different concentrations (mol%) of Cu+2 ions are shown in figure 7(a). In the EPR spectra, three weak parallel components are observed in the lower field region and the fourth parallel component is overlapped with the perpendicular component. The perpendicular components, in the high field region, are well resolved and are more intense. The number of spins participating in the resonance can be calculated with the help of Eq. (9). Figure 7(b) shows a plot of the number of spins participating in the resonance as a function of the concentration of Cu+2 ions in the CaAB glasses. From figure 7(b), it is clear that the number of spins increases monotonically with the increase of Cu+2 ions concentration in the glasses. At higher Cu+2 ions concentration, the hyperfine structure of perpendicular components diminished as a result of the individual line broadening which is due to the increased dipolar interactions with the ligand field fluctuations around the paramagnetic ion [64,65].
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Figure 7. (a) The EPR spectra of calcium alumino borate (CaAB) glasses doped with different Cu+2 ion concentrations; (b) A plot of number of spins as a function of Cu+2 ion concentration in the CaAB glasses [33].
In another example, when Cu+2 ions are added in a sodium potassium borate (NaKB) glasses, EPR spectra similar to those reported in other glass systems with Cu+2 ions are also observed. Figure 8(a) shows the EPR spectra of 0.5 mol% of copper ions in xNa2O-(30-x)K2O-70B2O3 (5 ≤ x ≤ 25) glasses with different compositions of mixed alkalis at 300 K. In the recorded spectra, it has been observed three weak parallel components in the lower field region and the fourth parallel component is overlapped with the perpendicular component; and the perpendicular components in the high field region are well resolved. It can be observed that the high field side of the spectrum is more intense than the low field side. These EPR spectra of Cu+2 ions studied could be analyzed by using the axial spin Hamiltonian of Eq. (2). The solution of the spin Hamiltonian gives the expressions for the peak positions related to the principal ‘g’ and ‘A’ tensors, as was shown in the previous section. By means of the EPR data can be calculated the paramagnetic susceptibility of the samples using Eq. (10). It is observed that the paramagnetic susceptibility shows mixed alkali effect and this is shown in figure 8(b). From the figure it is observed that the susceptibility decreases with x and reaches a minimum around x = 20 and thereafter increases with x, showing the mixed alkali effect in the glasses. The variation may be due to the structural changes with composition and also the modification of boron network with alkali content.
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Figure 8. (a) EPR spectra of 0.5 mol% Cu+2 ions doped in different mixed alkali borate glasses xNa2O-(30-x)K2O-70B2O3 (5 ≤ x ≤ 25), (b) the variation of paramagnetic susceptibility (χ) with x in different mixed alkali borate glasses xNa2O(30-x)K2O-69.5B2O3 + 0.5CuO (5 ≤ x ≤ 25); at room temperature [30].
4. Low-field microwave absorption in glasses with transition metal ions The low-field microwave absorption (LFMA) was first observed in 1987 in high-temperature superconductor ceramics [66-68]. This was followed by a large number of reports on not only high-temperature superconductor ceramics [69-72], but also including organic superconductors [73,74] and on conventional superconductors of both type-I and type-II [75-78]. Researches on LFMA response have shown that this signal is highly sensitive to the presence of a superconducting phase in the material under study. In figure 9(a-b) are shown examples of LFMA response for the conventional superconductor Pb and the ceramic superconductor YBa2Cu3O7-x, respectively. A typical LFMA response in Pb is shown in figure 9(a). Their lineshape describes the dynamics of microwave absorption between the Meisnner state and normal state, and it gives a good estimate of the critical field for mensuration temperature [75-77]. In the case of the ceramic YBa2Cu3O7-x, see figure 9(b), LFMA response shows a significant hysteresis loop in the superconductive state. Since the microwave induced dynamics of the fluxon is dissipative, it is not surprise at all that the field cycled LFMA
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Figure 9. LFMA response of a bulk sample of (a) Pb and (b) YBa2Cu3O7-x at 6.5 K and 30 K, respectively.
measurement shows an important hysteresis. The physical meaning of this hysteresis has been amply discussed in Refs [70,71]. In general, LFMA response is due mainly to the dissipative dynamics within Josephson junctions and/or to induced currents through weak links in these materials. Today, it is safe to assume that all superconductor exhibit LFMA response (which has been confirmed experimentally). The reverse statement, that any material exhibiting LFMA response is a superconductor, is in general not true. Recent studies have shown that non-superconducting materials also show LFMA response [79-91]. This signal may be caused not only by superconductivity, but also by any phenomena associated with magnetic-field-dependent microwave losses in the materials. In the case of heavily doped semiconductors, the LFMA response (figure 10) is due to magnetoresistance phenomena [79-83], i.e. magnetoresistive effects are responsible for the magnetic-field dependence of the microwave absorption in semiconductors. This assertion is based on the fact that microwave absorption (P) is proportional to sample resistance (R), P ∼ R and dP/dH ∼ dR/dH where H is the magnetic field, for this kind of materials [79-83]. The existence of the LFMA response has also been reported in soft magnetic materials such as amorphous ribbons [84-86], glass-coated microwires [87,88] and multilayers [89-91]. In these works, the central role of the anisotropy field in LFMA response has been recognized, as well as its general correlation with magnetization processes at low fields. A similarity between LFMA response and magnetoimpedance (MI) has been observed [84-90], as is shown in figure 11, where MI is defined as the change of the
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impedance of a magnetic conductor subjected to an ac excitation current, under the application of a dc magnetic field; showing that LFMA response can be caused mainly by the magnetization process, which strongly depends on the anisotropy field, as in MI.
Figure 10. LFMA response of a heavily doped semiconductor, in the range from -50 to 50 Gauss, at temperatures (a) 3.1 K y (b) 10 K [79].
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Figure 11. (a) VSM hysteresis loop, (b) magnetoimpedance curves at a frequency of 50 MHz, and (c) LFMA response. All data correspond to an amorphous Co66Fe4B12Si13Nb4Cu alloy sample.
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Now consider the case of glasses with transition metal ions, a LFMA response has been detected at low temperatures in glasses doped with Fe and Cu [92,93]. Figure 12 shows spectra for OPS-1 glass doped with 7% of Fe2O3 (figure 12(a)) and 10% of CuO (figure 12(b)). Both spectra contain at T = 3 K (curves 1) a signal centred around zero field with phases opposite to the phases of the EPR lines of Fe+3 and Cu+2. These results were interpreted in terms of local superconductivity. In recent studies has been observed a sharp LFMA response for Mndoped Na2O–CaO–MgO–SiO2 glasses (≤ 1% doping level) [28,29]. For this kind of silicate glasses, a sharp LFMA response is observed with a phase opposite to paramagnetic resonances due to Mn+2 ions; with g ≈ 4, 3 and 2 at magnetic field values of about 1350, 2250 and 3400 G, respectively, as is shown in figure 13(a). For this kind of glass, LFMA response exhibits a nonresonant nature, with a minimum value near zero magnetic field that increases to a fixed value as the magnetic field is increased, as is shown in figure 13(b); in others words, this is a non-resonant microwave absorption induced by the magnetic field. This non-resonant absorption is caused by the introduction of manganese in the glass network, where LFMA response can be distinguished from the regular EPR spectrum due to different dependence of the signal magnitude on microwave power and temperature. The microwave absorption in glasses can be originated from dielectric losses due to electric charge displacement [22]. The time-averaged power, P,
Figure 12. Derivative microwave absorption for the OPS-1 glass doped with (a) 7 wt% of Fe2O3 and (b) 10 wt% of CuO at T= 3 K (curve 1) and T= 20 K (curve 2) [92,93].
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Figure 13. Microwave absorption of the Na2O–CaO–MgO–SiO2 glass doped with 0.1 wt% MnO2 at 77 K. (a) Extended signal (EPR spectrum more LFMA response) and (b) numerical integration of the LFMA response [28,29].
dissipated in a system carrying a current density j in an alternating electric field, E = E0 e(-iωt), can be expressed as [94]: P = ½ ω ε0 Im(ε)E02
(11)
where ε0 is the dielectric constant of free space, Im(ε) is the imaginary part of the dielectric constant, and ω = 2πf, where f is the frequency. It can be observed that the microwave power absorption varies linearly with frequency and the imaginary part of the dielectric constant, and with the square of the microwaves electric field intensity. For a constant frequency (and amplitude) of applied field, the microwave power absorption should follow a behavior similar to Im(ε). Let me remember that in a dielectric material the Maxwell displacement current, j = d(εε0E)/dt, is induced by the microwave electric field E. Since j = σE, where σ is the microwave conductivity (σ = ½ε0Im(ε)ω), can describe himself the magnetic field dependence of the microwave absorption, P = σE02, in terms of changes in microwave conductivity σ(H) with an applied static magnetic field H. Experimentally the observed microwave power absorption due to electric dipoles, is ∆P = P(H)-P(0) = ∆σE02
(12)
where ∆σ = σ(H)-σ(0) is the change in the microwave conductivity induced by the magnetic field H. Since dielectric loss in absence of static magnetic field is given by P(0) = σ(0)E02, the observed response can be written,
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∆P = [∆σ/σ(0)] P(0)
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(13)
The term ∆σ/σ(0) describe relative changes in microwave conductivity induced by the external field, i.e. magnetoconductance. Additionally, a large magnetoconductance effect (a sharp decrease of electric resistance induced by an applied magnetic field) has been detected in perovskite manganites [95,96]. In these materials, this effect is explained by enhanced electron hopping migration occurring via a double exchange mechanism in mixed valence Mn+3-O-Mn+4 structure with an additional magnetic coupling energy that provides ferromagnetism. In the present case, the low-field microwave absorption by electric dipoles should be considered as the enhancement of dielectric loss by the external magnetic field, or microwave magnetoconductance, which leads to: dP/dH = [P(0)/σ(0)] dσ/dH
(14)
where the factor P(0)/σ(0), the square of the microwave electric field E02, is constant. In summary, LFMA response is described in terms of spin-dependent dielectric loss, or microwave magnetoconductance, that derives from the tunneling charge migration between oxygen atoms via a paramagnetic dopant ion [28,29].
5. Acknowledgements Support from project of complementary support for SNI 1 of CONACyT (No.89780) is gratefully acknowledged. The author acknowledges a postdoctoral fellowship from UNAM-Mexico.
6. Conclusions In this work is shown that EPR is the most powerful spectroscopic method available for obtaining local structural information and symmetry of transition metal ions incorporated in the glass network. LFMA response provides information on non-resonant microwave absorption around zero field in glasses, more important, this signal can detect the dissipative dynamics of microwave absorbing centers, providing valuable information about the nature of these materials. EPR and LFMA techniques are powerful tools for the research of glasses at microwave frequencies.
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